My kids lean toward more upbeat songs, and they love oldies. My daughter's favorites are ElvisPresleyTeddyBear, The Four Seasons Big Girls Don't Cry, FrankieValli Can't Take My Eyes Off Of You... My kids LOVEFrankieValli and The Four Seasons.
When they were infants and at bedtime, their songs were/are always You Are My Sunshine, Amazing Grace, and Smile (CharlieChaplin). Smile is my favorite.

I've been working on this myself, so my list is rather long, and I didn't even include all of them. Very few are for babies, some are about the musicians children, but most just gives me a childhood feeling or something I know babies or toddlers/children enjoy (have a few godchildren who spend a lot of time at our house).

I'm not sure if this is what you're looking for, but I have many fond memories of my mother singing All the Pretty Little Horses to me when I was growing up. There's a version on iTunes by BeckyJeanWilliams that's just hauntingly beautiful. I also really like River Flows in You by Yiruma and Butterfly Waltz by BrianCrain. I'll post again if I find any more. This is a fantastic thread, by the way!